1064. Complete Binary Search Tree (30)

A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

• The left subtree of a node contains only nodes with keys less than the node's key.
• The right subtree of a node contains only nodes with keys greater than or equal to the node's key.
• Both the left and right subtrees must also be binary search trees.

A Complete Binary Tree (CBT) is a tree that is completely filled, with the possible exception of the bottom level, which is filled from left to right.

Now given a sequence of distinct non-negative integer keys, a unique BST can be constructed if it is required that the tree must also be a CBT. You are supposed to output the level order traversal sequence of this BST.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=1000). Then N distinct non-negative integer keys are given in the next line. All the numbers in a line are separated by a space and are no greater than 2000.

Output Specification:

For each test case, print in one line the level order traversal sequence of the corresponding complete binary search tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.

Sample Input:

101 2 3 4 5 6 7 8 9 0

Sample Output:

6 3 8 1 5 7 9 0 2 4 

思路：而对于任意一棵搜索树，其中序遍历的输出，是一个递增的数列。用qsort函数将输入的数列递增排序，得到了完全二叉搜索树的中序遍历输出，得到数组a[i]。根据centertolevel函数求得层序b[i]。其中b[i]满足完全二叉树性质，孩子节点的下标为i  (i从1开始),则其左孩子节点的下标为2*i，右孩子节点的下标为2*i+1

#include<iostream>#include<cstdlib>#define max 10001using namespace std;struct TreeNode{int data;TreeNode *left;TreeNode *right;};int a[max],b[max];//全局 int n,j=0;//全局 int cmp(const void * a,const void * b){return *(int *)a-*(int *)b; }void centertolevel(int root){if(root<=n){  //这里是root<=n而非j<n centertolevel(2*root);b[root]=a[j++];centertolevel(2*root+1);}}int main(){freopen("input.txt","r",stdin);int i; bool flag=false;cin>>n;for(i=0;i<n;i++)  cin>>a[i];qsort(a,n,sizeof(int),cmp);centertolevel(1);for(i=1;i<=n;i++){if(!flag) flag=true;else cout<<" ";cout<<b[i];}return 0;}